Math 514 homework #24 Due date: 19951120 D. J. Bernstein 19951113 Exercise 76. Let α be a complex number such that α^{3} = α + 1. Prove that Z[α]^{∗} is generated by −1 and α. Exercise 77. Let α be a complex number such that α^{3} = 5α + 1. Prove that Z[α]^{∗} is generated by −1, α, and α + 2.